Sentence examples similar to self path from inspiring English sources

Suppose that G has an end point x0 and T is a self-path map.

Note that T is a self-path map which has no fixed point.

Then G has a start set if and only if each self-path map on G has a fixed set.

Then G has an end point if and only if each self-path map on G has a fixed point.

We say that T is a self-path map whenever x∈ [ T x] G for all x∈G.

Therefore, from the definition of self-path map, we have (Din[T(D ]_{G}), which implies that (Din G^{prime}).

Now assume that G is a directed graph and each self-path map on G has a fixed point but has no end point.

Since x∈ [ T x] for all x∈G′, T x∈ [ T2x] G and so T is a self-path map on G′.

Then it is easy to see that T is a self-path map but G has no fixed set and no start set either.

Our next example shows that indeed if a directed graph has no start set, then a self-path map may be defined which has no fixed set.

Further, the notion of a self-path set valued map is defined and its relation with the start set is established.